Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications

Know about the book -

Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications is written by Mark Lʹvovich Agranovskiĭ and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 0821897470 (ISBN 10) and 9780821897478 (ISBN 13).

This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. The author obtains classifications of translation-invariant spaces and algebras of functions on semisimple and nilpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains. When such classifications are possible, they lead in many cases to new characterizations of the classical function spaces, from the point of view of their group of admissible changes of variable. The algebra of holomorphic functions plays an essential role in these classifications when a homogeneous complex or $CR$-structure exists on the manifold. This leads to new characterizations of holomorphic functions and their boundary values for one- and multidimensional complex domains.